"I like Mitch, but for eight years we've been saying we're going to repeal and replace Obamacare – it's not like we made this up overnight," Graham told "The Brian Kilmeade Show," per The Hill.

"We have been working on repealing Obamacare all year. The idea put forward didn't pass, it was in many ways an ill-conceived idea."

The debate on healthcare has divided Washington ever since former President Barack Obama signed the Affordable Care Act into law in 2010. Now that Republicans control both the executive and legislative branches, they have tried — and failed — to pass legislation this year that would repeal and replace Obamacare.

Graham said he is frustrated the party cannot come to an agreement on how to fix the nation's healthcare system.

"There is no way to sugar coat this. The Republican Party promised for eight years to repeal and replace Obamacare," Graham said. "We failed, and if we give up, shame on us."

President Donald Trump also criticized McConnell on Wednesday, asking why he was not able to pass healthcare legislation after he has had nearly a decade to come up with a plan.